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ANALYTICAL MECHANICS
a
The sum of all the forces acting upon a body plus the linear kinetic reaction equals zero, or the resultant of all the forces acting upon a body equals and is opposite to the linear kinetic reaction.
Sum of all forces + linear kinetic reaction = OJ     /A A or   Resultant force = —(linear kinetic reaction).    J
Now let us apply the law to the experiment of the preceding section. After the block is released it is acted upon by three forces, namely, its weight, the reaction of the table, and the pull of the string. The law states that the resultant of these forces equals the kinetic reaction of the block and is oppositely directed. Since the weight and the reaction of the table are exactly balanced the pull of the string is the resultant force. Therefore the kinetic reaction of the block equals the pull of the string and has a direction opposite to that in which the block is pulled.
94. Definition of Mass. — In the block experiment suppose the free end of the string to be connected to a spring balance which is fixed on the table, Fig. 59. Further suppose the block to be set in motion as in the previous experiment. Let one person observe the readings of the balance and another the acceleration of the block. If FI, F2, F*, etc., denote the readings of the balance and /i, /2, /3, etc., the values of the acceleration of the block, obtained simultaneously with the readings of the balance, then it will be found that the following relations hold true:
F1 __ FZ        j^3
/I  " /»   ~ /3   ""   '    '
FIG. 59.
-•m,
(i)```